Search results for "15A09"

showing 2 items of 2 documents

The diamond partial order in rings

2013

In this paper we introduce a new partial order on a ring, namely the diamond partial order. This order is an extension of a partial order defined in a matrix setting in [J.K. Baksalary and J. Hauke, A further algebraic version of Cochran's theorem and matrix partial orderings, Linear Algebra and its Applications, 127, 157--169, 1990]. We characterize the diamond partial order on rings and study its relationships with other partial orders known in the literature. We also analyze successors, predecessors and maximal elements under the diamond order.

Pure mathematics15A09Principal ideal010103 numerical & computational mathematicsengineering.material01 natural sciencesCombinatoricsMatrix (mathematics)Linear extensionPrincipal ideal0101 mathematicsCiências Naturais::MatemáticasMathematicsRing (mathematics)RingAlgebra and Number TheoryScience & Technology010102 general mathematicsAnells (Algebra)DiamondOrder (ring theory)Sharp partial orderStar partial orderMinus partial order06A06Linear algebraengineeringÀlgebra linealMATEMATICA APLICADAMaximal element:Matemáticas [Ciências Naturais]
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Special elements in a ring related to Drazin inverses

2013

In this paper, the existence of the Drazin (group) inverse of an element a in a ring is analyzed when amk = kan, for some unit k and m; n 2 N. The same problem is studied for the case when a* = kamk-1 and for the fk; s+1g-potent elements. In addition, relationships with other special elements of the ring are also obtained

Pure mathematicsDrazin inverse16E50Inverse010103 numerical & computational mathematicsInvolutory element01 natural sciencesSecondary: 16A300101 mathematicsMathematicsRingRing (mathematics)Science & TechnologyAlgebra and Number TheoryGroup (mathematics)Primary: 15A09010102 general mathematicsAnells (Algebra)15A09 [Primary]PowerDrazin inverseÀlgebra linealElement (category theory)16A30 [Secondary]Unit (ring theory)Linear and Multilinear Algebra
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